Question

1.Calculati media aritmetica si media geometrica a numerelor $\sqrt{ 7- 4\sqrt{3}$ si $\sqrt{ 7+ 4\sqrt{3}$
2. Calculati $[ \frac{1}{4} ] + [ \frac{2}{4}]+[ \frac{3}{4} ]+...+[ \frac{100}{4}].$

Answer 1

1) √( 7-4√3)= √(7-√48)

A=7
B=48
C²=49-48=1  

√(7-√48)= √(7+1)/2 - √(7-1)/2= √8/2 - √6/2=  √4 -√3=  2-√3

ma= (2-√3+2+√3)/2=  4/2=2

mg= √ab=  √(2-√3)(2+√3)=  √4-3=1

2) 1/4 + 2/4 + 3/4+...+ 100/4=

=[(1+100)*100/2 ]/4=

= (101*50)/4=

=101* 25/2=

=2525/2=  1262,5